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6.

Find the values of a and b, where a and b are real, given that (a + bi)(2 – i) = 5 – i.


2. Find the complete integral of the partial differential

equation p+q=sin x+sin y.


Find the complete integral of the partial differential

equation pq = 2



differentiate

f(x) = 2 + |x|2/3

let the function f definedbe defined as: f(x)= 4a if x</=-2, 3x^2 if -2<x</=1, x+b if x>1. Determine the values of the consonants a,b, so that f is continuous at x=-2 & x=1
use squeeze theorem to show that: limit as x approaches infinity of (sin(e^x))/x =0, hense evaluate the limit as x approaches infinity of (sin(e^x))/sqr(x^2+2)

Draw graphs of the following functions.


(a)

f: R—>R defined by f(x) = Floor(x)

(b)

f: R—>R defined by f(x) = Ceiling(x)



The weekly sales (RS) at a big store x weeks after the end of an advertising campaign are given


by S(x)= 5000+


5000


X+5 Find the sale for the indicated week's limits


a) S(2),


b) lim S(x)


An office supply company sells Q permanent markers per year at $P per marker. The price-demand equation for these markers is P=10-0.001Q. The total cost of manufacturing Q permanent markers is TC(Q)=5000+2Q.


A. What is the company's maximum profit?B. What should the company charge for the markers, and how many markers should be produce to maximize the profit?

Find the inverse Laplace transforms of the following functions:

(a)

s + 3 /(s^2 + 6s + 13)

(b)

2s + 3/(s^2+6s+13)


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